傅里葉分析

內容概要

傅里葉變換是在數字信號處理方面很有用的一個方法，在通信和信息專業(yè)有很強的應用。本書總結、整理了近50年來傅里葉分析理論研究的基本成果，系統(tǒng)性強，內容先進全面。    作者Loukas Grafakos，希臘雅典人，在加利福尼亞大學洛杉磯分校獲得博士學位，現(xiàn)任密蘇里州大學數學教授。曾因出色的教學被授予Kemper Fellow獎，自著或與人合著了40篇傅里葉分析方面的文章。    本書內容包括Lp空間和插值，極大函數，傅里葉變換以及廣義函數，一維環(huán)群上的傅里葉分析，卷積型奇異積分，Littlewood-Paley理論與乘子，光滑性和函數空間，BMO和Carleson測度，非卷積型奇異積分，加權不等式，傅里葉積分的有界性和收劍性。講述方式易于接受，只要有本科知識就能夠閱讀，各章節(jié)有預備知識提要，習題例題豐富，稱得上一本優(yōu)秀的教材。最后提供了574篇文獻目錄，讀研究人員也很有必要。

作者簡介

作者：（美國）格拉法科斯

書籍目錄

出版說明序PrefaceChapter 1 Lp Space and Interpolation  1.1 Lp and Week Lp 1.2 Convolution and Approximate Identities 1.3 Interpolation 1.4 Lorentz SpaceChapter 2 Maximal Functions ,Fourier Transform ,and Distributions  2.1 Maximal Functions 2.2 The Schwartz Class and the Fourier Transform 2.3 The Class of Tempered Distributions 2.4 More about Distributions and the Fourier Transform 2.5 Convolution Operators on Lp Spaces and MultipliersChapter 3 Fourier Analysis on the Torus 3.1 Fourier Coefficients 3.2 Decay of Fourier Coefficients 3.3 Pointwise Convergence of Fourier Series 3.4 Divergence of Fourier Series and Bochner-Riesz Summablility 3.5 The Conjugate Function and Convergence in Norm 3.6 Multipliers ,Transference,and Almost Everywhere Convergence  3.7 Lacunary SeriesChapter 4 Singular Integrals of Convolution Type 4.1 The Hibert Transform and the Riesz Transforms 4.2 Homogeneous Singular Integrals and the Method of Rotations 4.3 The Calderon-zygmund Decomposition and Singular Integrals 4.4 Sufficient Conditions for Lp Boundedness 4.5 Vector-Valued Inequalities 4.6 Vector-Valued Singular IntegralsChapter 5 Little wood-paley Theory and Multipliers 5.1 Little wood-paley Theory  5.2 Two Multiplier Therrems 5.3 Applications of Little wood-paley Theory  5.4 The Haar System,Conditional Expectation,and Martingales  5.5 The Spherical Maximal Function 5.6 WaveletsChapter 6 Smoothness and Function Spaces  6.1 Riesz Potentials ,Bessel Potentials ,and Fractional Integrals  6.2 Sobolev Spaces 6.3 Lipschitz Spaces 6.4 Hardy Spaces 6.5 Besov-Lipschitz and Triebel-Lizorkin Spaces 6.6 Atomic Decomposition 6.7 Singular Integrals on Function SpacesChapter 7 BMO and Carleson Measures 7.1 Functions of Bounded Mean Oscillation 7.2 Duality Between H1 and Carleson Measures 7.3 Nontangential Maximal Functions and Carleson Measures ……Chapter 8 Singular Integrals of Nonconvolution TypeChapter 9 Weighted IntequalitiesChapter 10 Boundedness and Convergence of Fourier IntegralsAppendix A Gamma and Beta FunctionsAppendix B Bessel FunctionsAppendix C Rademacher FunctionsAppendix D Spherical CoordinatesAppendix E Some Trigonometric Identities and InequalitiesAppendix F Summation by PartsAppendix G Basic Functional AnalysisAppendix H The Minimax LemmaAppendix I The Schur LemmaAppendix J The Whitney Decomposition of open sets in RnAppendix K Smoothness and Vanishing MomentsBibliographyIndex of NotationIndex 教輔材料申請表

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